TY - JOUR AU - Shivanian, E. AU - Abdolrazaghi, F. PY - 2015 TI - On the Existence of Multiple Solutions of a Class of Second-order Nonlinear Two-point Boundary Value Problems JO - Journal of Mathematics and Computer Science SP - 97-107 VL - 14 IS - 2 AB - A general approach is presented for proving existence of multiple solutions of the second-order nonlinear differential equation \[u'' (x) + f (u(x)) = 0,\quad x\in [0,1], \] subject to given boundary conditions: \(u(0) = B_1, u(1) = B_2\) or \(u'(0) = B'_1, u(1)=B_2\). The proof is constructive in nature, and could be used for numerical generation of the solution or closed-form analytical solution by introducing some special functions. The only restriction is about \(f(u)\) , where it is supposed to be differentiable function with continuous derivative. It is proved the problem may admit no solution, may admit unique solution or may admit multiple solutions. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.014.02.02 DO - 10.22436/jmcs.014.02.02 ID - Shivanian2015 ER -